Answer:
(a) f(1) = ft(3) = 53 ft
(b) t = 2.156 s
Step-by-step explanation:
The function for the height of the ball is:
[tex]f(t) = -16t^2 + 64t + 5[/tex]
(a) For t = 1s
[tex]f(1) = -16*1^2 + 64*1 + 5\\f(1) = 53\ ft[/tex]
For t = 3s
[tex]f(3) = -16*3^2 + 64*3 + 5\\f(3) = 53\ ft[/tex]
Therefore, f(1) = f(3)
(b) According to Rolle's Theorem, if the function yields the same height in two distinct points, there must be a stationary point between them, that is, a point where the velocity is zero.
The velocity function is found by differentiating the height function:
[tex]f'(t) = -32t + 64 + 5\\[/tex]
When the velocity is zero:
[tex]0= -32t + 64 + 5\\t=2.156\ s[/tex]
